## Real Estate Investment: The Spectral Risk Measure

Combining subjective risk aversion with data is possible through the use of so-called "coherent risk measures" (Artzner, Delbaen, Eber and Heath, 1999). One of these is the Spectral Risk Measure (SRM) which computes the inner product of a vector of probabilities generated from a suitable risk aversion function and a vector of outcomes.

This is an extension of the often used "Best Case - Worst Case - Most Likely" method of computing an expectation. In the graphic, using a convex risk aversion function, we see the mean of a number of outcomes (on the right) and the SRM (on the left). The series of bubbles show the size of the weight given to each outcome. Consistent with risk aversion theory, the greatest probability is given to the worst outcome.